The first four movies before The Avengers were all about someone having the ability to be a hero but not the qualities until he had to step up to the challenge: Iron Man 1 was about the egotistic genius billionaire Tony Stark seeing first hand what his weapons were doing to innocents and being unable to use the normal means to stop it, so he had to use the Iron Man armor to stop the terrorists (and Stane) and destroy the weapons himself; The Incredible Hulk was about Banner trying to cure himself of Hulk until Abomination entered the frame, at which point he renounced to any future attempt to get a cure so he'd be able to stop him and any other possible gamma monster; Iron Man 2 was about a dying Tony choosing Pepper and Rhodey as his successors as CEO of Stark Industries and Iron Man and getting them to step up to the challenge; Thor is about Thor stopping being selfish and learning humility. Then we have Captain America: The First Avenger, that is about the opposite: Steve wants to make a difference and stop the Nazis, but first lacks the powers (being a skinny runt before becoming the Super Soldier) and then the occasion, and has to take them, becoming a hero in the process.
Some might wonder why Coulson simply didn't shoot the robbers in A Funny Thing Happened on the Way to Thor's Hammer. Well, police are a lot more interested when a couple of punks end up with bullet holes than they are when some mystery man simply beats them up.
And the little "tae bo" story means they won't bother searching for him, just think the clerk did it. He may have also not shot because he worried the bullet might go through them and hit the clerk.
Coulson is also one of the good guys from a series of superhero movies. Those types generally avoid lethal force if it's not necessary, and it was obviously not necessary in that short.